For example, matching with preferences typically assumes that only ordinal utilities can be elicited.
Ordinal utilities provide only the rankings of utilities received from different bundles of goods or choices. It does not require individuals to specify how much extra utility they received from the preferred bundle of goods or services in comparison to other bundles. Decision-makers are only required to tell which bundles they prefer. While cardinal preferences can be challenged, eliciting only ordinal preferences is much less controversial in applications such as school choice or kidney exchanges. The Gale-Shapley algorithm [1]} is arguably the most well-known example, which takes ordinal preferences as an input and computes a stable outcome. Importantly, the mechanism is strategy-proof for one side of the market. The Top Trading Cycles algorithm [2]} for the housing market enjoys the same property, but also here, preferences are restricted to unit demand.
